Following buzz that the Gilt City Hamptons House could be shut down by East Hamp ton residents who objected to poolside parties, screenings and dinners, the activities will go on after all — but at a different location. Sources say the Gilt-curated events, including a movie screening with Katie Lee and dinner with Scarpetta chef Scott Conant, have been moved to a Bridgehampton site. The first events will kick off this weekend, including a Sunday dinner with the restaurant-owning Scotto family. A Gilt rep said, “We are pleased the private events will open on time as planned.”